Home/Algebra/Eigenvalues and diagonalization/Powers via diagonalization20. Eigenvalues and diagonalizationPowers via diagonalizationLevel: avanzadoIn 20. Eigenvalues and diagonalizationFormulaCopy LaTeXAn=PDnP−1A^n=PD^nP^{-1}An=PDnP−1Tagsalgebraeigenalgebra formulalinearvalues eigenDetailSimplifies matrix powers and recurrences.Explore the ideaFound an error? Contact us.Related formulasRelatedDiagonalizationA=PDP−1A=PDP^{-1}A=PDP−1Open formulaOpen in sectionRelatedSecond-order linear recurrencean=c1an−1+c2an−2;r2−c1r−c2=0a_n=c_1a_{n-1}+c_2a_{n-2};\quad r^2-c_1r-c_2=0an=c1an−1+c2an−2;r2−c1r−c2=0Open formulaOpen in section